The present invention relates to an SSMA (Spread Spectrum Multiple Access) data transmission system in which each binary information signal (k.sub.ij) is multiplied with a binary function or with an address a.sub.i (t-j T) having Z binary digits and is transmitted possibly after being modulated on a carrier oscillation cos (.omega..sub.i t), and wherein the m.sup.th user station at the receiving end determines the interfered with receiving function K.sub.m *(t) intended for that station by correlating the total received function mixture signal f.sub.e (t) with the carrier-modulated address signal g*a.sub.m (t) for that particular station.
A number of possibilities have long been known in the art whereby a plurality of stations may communicate with one another over a common transmission channel without mutual interference. For example, it is known to divide the transmission band into partial frequency bands (frequency multiplex) or to associate time spots in a PCM raster to the individual stations (time multipliex).
A new method for achieving this result is also known which is called the SSMA method (time function multiplex). A system using the SSMA method is described, for example, in the article "Modulation Techniques for Multiple Access to a hard-limiting Satellite Repeater" by J. W. Schwartz, J. M. Aein, and J. Kaiser; Proceedings of the IEEE, Vol. 54, No. 5, May 1966, Pages 763-776. In this method the information is first digitalized (PCM or .DELTA.-modulation) and then each binary signal k.sub.ij (low frequency band b) is multiplied with a binary function or address a.sub.i (t-jT) having Z binary digits. During the duration of a data binary signal T, Z address binary digits are thus transmitted which corresponds to a spread of the low frequency band b to the value B = Z .multidot. b. The function K.sub.i (t) .multidot. a.sub.i (t-jT) is then carrier-modulated so that the function or signal f.sub.i (t) = K.sub.i (t) .multidot. a.sub.i (t-jT) .multidot. cos(.omega..sub.i t) is being transmitted. The function f.sub.i (t) requires the entire bandwidth of the transmission channel. The transmitting functions of all stations are thus additively superimposed so that each station receives the total mixture signal f.sub.e (t) where ##EQU1##
For station m the signals in the received signal f.sub.e (t) other than the desired signal f.sub.m (t), i.e., the function ##EQU2## thus represents an interference which almost has a noise characteristic. When each transmitting station connected to the transmission channel provides a signal which produces an output signal S.sub.E at each receiver site, and the channel has its own noise R, each receiver receives its useful signals with a signal-to-noise ratio S/N of ##EQU3## for the situation of n stations transmitting simultaneously. For the station m, by means of a correlation process, the function K.sub.m *(t), which represents the error-containing transmitted function K.sub.m (t), is reproduced from this noise with a signal-to-noise ratio of ##EQU4##
The function K.sub.m *(t) is usually produced by multiplying the received mixture signal f.sub.e (t) with the carrier-modulated address signal for the station m EQU g*a.sub.m (t) = a.sub.m *(t - jT - .tau..sub.m *) cos (.omega..sub.m *t - .phi..sub.m *),
where g* a.sub.m (t) is the address with carrier in the receiving station m not yet exactly sychronized and carrier-controlled to the received addresses and for the case where EQU g* a.sub.m (t) = ga.sub.m (t),
where ga.sub.m (t) is the synchronized and controlled sequence of addresses the following results: ##EQU5## where k.sub.mj * is the transmitted binary signal k.sub.mj falsified by the interfering value [f.sub.e (t) - f.sub.m (t)] .multidot. g a.sub.m (t). The closer this interfering value compares to f.sub.m.sup.2 (t), the greater becomes the probability of an error for k.sub.mj *. Difficulties in the SSMA method existed in the derivation of g*a.sub.m (t) .apprxeq. ga.sub.m (t) and in the determination of the most favorable function collective a.sub.i (t - jT). These problems have been solved to an almost satisfactory degree. Theoretically, however, ##EQU6## can only be realized by an orthogonal function system (e.g., Walsk functions). Such a system is of no use, however, since it leads to unsurmountable synchronizing difficulties. Thus, according to the present state of the art, SSMA has the drawback, when compared with the orthogonal frequency multiplex and time multiplex methods, of producing interference inherent to the system which principally means a reduction of the channel capacity compared to the older methods.
Since, however, SSMA offers a number of other advantages, e.g., for synchronization problems, a simple way of assuring the secrecy of the transmitted data, and few filtering problems, as compared to the older methods, it is desirable in many instances to utilize this method.